Researchers at Birkbeck, University of London and King's College London questioned 715 parents about their child's daily touchscreen use and sleep patterns. They found that babies and toddlers who spent more time using a touchscreen slept less at night and, despite sleeping more during the day, slept for less time overall.
Sleep is important for the development of the brain, especially during the first few years of life, when "neural plasticity" is at its greatest.
The study could not prove a causal link between use of the devices and shortened sleep, as it relied on parents' records. But researchers said there were four potential mechanisms which could be taking effect.
These include the impact of blue light, which can affect the body clock, and the stimulation caused by the content of the games or programs. Infants and toddlers might also be spending less time sleeping because they were staying up later on devices. Fourthly, children who particularly sought out longer time on such gadgets might be more likely to suffer from other conditions such as hyperactivity.
Previous research by the same team has found that babies and toddlers who used iPads had superior motor skills to those who did not.
Dr Tim Smith, from Birkbeck, said: "There is so much cognitive development going on at that stage that it's possible any influence would have an amplifying effect."
The team is planning new studies to try to establish whether there is a causal relationship between use of touchscreen devices and sleep.
Smith said it was difficult to give clear advice to parents because the science was so immature.
But he said it was sensible to allow almost no screen use for those below the age of 18 months, apart from "video chat" such as Skype.
Other scientists said findings should be interpreted with "extreme caution". Dr Andrew Przybylski, experimental psychologist and research fellow at the Oxford Internet Institute, University of Oxford, said the fact parents were told in advance about the purpose of the research could have skewed the results.